CUSUM multi-chart based on nonparametric likelihood approach for detecting unknown abrupt changes and its application for network data

This article deals with the online monitoring of changes when the distributions (including the form of distributions) of pre-change and post-change are unknown. We not only construct a nonparametric CUSUM multi-chart based on the nonparametric likelihood function to deal with the online change detection problem, but also give a strategy for choosing the appropriate value if we choose only one truncated value of u. And under the measurement called nonparametric Control chart Performance Index (CPI), we show an asymptotic optimal design for the allocation of the reference post-change Cumulative Distribution Functions (C.D.F.s). Finally, we use simulated data to present the related results. Moreover, we apply the method in this paper to network data, which is very common at present.

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